Allocating Resources in a Frequency-Time Space to Mobile Station Data

ABSTRACT

To allocate resources in an orthogonal frequency domain multiple access (OFDMA) system, two-dimensional rectangular regions are assigned in a frequency-time space to data bursts associated with mobile stations. At least one data burst does not fit in an available space in the frequency-time space is determined. In response to the determining, the assigned two-dimensional rectangular regions are reshaped.

CROSS-REFERENCE TO RELATED APPLICATIONS

This claims the benefit under 35 U.S.C. §119(e) of U.S. ProvisionalApplication Ser. No. 60/869,273, entitled “Efficient Implementation ofWiMax Downlink Scheduler,” filed Dec. 8, 2006 (having Attorney DocketNo. (18701ROUS01U), which is hereby incorporated by reference.

TECHNICAL FIELD

The invention relates to allocating resources in an orthogonal frequencydivision multiple access system.

BACKGROUND

Orthogonal frequency division multiple access (OFDMA) allows formultiple users to share wireless resources of a wireless communicationsnetwork in both frequency and time. A standard for OFDMA operation isaccording to IEEE (Institute of Electrical and Electronics Engineers)802.16e. According to OFDMA, different users can be assigned differentsets of subcarriers (at different frequencies), where the subcarriersare closely-spaced orthogonal subcarriers, with each subcarriermodulated with a modulation scheme. Each group of subcarriers assignedto a user is referred to as a subchannel.

According to OFDMA, a data region (also referred to as a data burst)that is to be communicated across the forward or downlink wireless linkbetween a base station and a mobile station is provided with atwo-dimensional allocation of a group of contiguous subchannels(frequency axis) within a group of contiguous OFDMA symbols (time axis).The allocated data region can be visualized as a rectangle, where therectangle is made up of a number of subchannels in the subchannel axis(e.g., vertical axis) and a number of OFDMA symbols (e.g., horizontalaxis).

An issue associated with allocation of OFDMA resources (including OFDMAsymbols and subchannels) is that there is limited flexibility in howOFDMA resources are allocated to data bursts associated with differentusers in rectangular regions in frequency and time.

SUMMARY

In general, according to an embodiment, a method is provided forallocating resources in an orthogonal frequency domain multiple access(OFDMA) system, where two-dimensional rectangular regions are assignedin a frequency-time space to data bursts associated with mobilestations. In response to determining that at least one data burst doesnot fit in an available space in the frequency-time space, the assignedtwo-dimensional regions are re-shaped.

Other or alternative features will become apparent from the followingdescription, from the drawings, and from the claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of a network arrangement that includes mobilestations and a base station, in which some embodiments of the inventioncan be incorporated.

FIG. 2 illustrates an example frame containing rectangular regionsassigned to data bursts, according to an embodiment.

FIG. 3 is a flow diagram of a process of assigning rectangular regionsin a frequency-time space, according to an embodiment.

FIG. 4 is a flow diagram of a process of shaping rectangular regions,according to an embodiment.

DETAILED DESCRIPTION

In the following description, numerous details are set forth to providean understanding of some embodiments. However, it will be understood bythose skilled in the art that some embodiments may be practiced withoutthese details and that numerous variations or modifications from thedescribed embodiments may be possible.

In accordance with some embodiments, allocation of resources in anorthogonal frequency domain multiple access (OFDMA) system is providedin which use of resources in a frequency-time space is optimized basedon application of a shaping algorithm and fitting algorithm to fit asmany data bursts associated with mobile stations as possible into theavailable space of the frequency-time space. According to OFDMA, afrequency-time space (or frequency-time domain) is defined bysub-carriers at different frequencies (on one axis) and OFDMA symbols atdifferent times (on a second axis). Along the time axis, a sequence ofOFDMA symbols is provided, where each symbol is associated with aparticular symbol time duration. In one implementation, the OFDMA systemis according to the protocol defined by IEEE 802.16e. Note that in otherimplementations, other types of OFDMA technologies can be used.

In the downlink path, from the base station to mobile stations, databursts communicated from the base station to the mobile stations areeach allocated a rectangular region of the frequency-time space ofresources. In other words, each data burst takes up consecutive logicalsubchannels and consecutive OFDMA symbols. A subchannel is made up of agroup of subcarriers at different frequencies. In the uplink direction(from mobile station to base station), data bursts may benon-rectangular two-dimensional regions in the frequency-time space. Inthe 802.16e standard, for example, normal uplink data bursts areallocated a number of allocation units termed slots. A slot is a logicalfrequency domain subchannel available for a fixed number of symbols.Slots are allocated in a time-first order starting from the lowestnumber subchannel on the lowest number symbol.

In the ensuing discussion, reference is made to allocating resources inthe frequency-time space for downlink data bursts (from the base stationto the mobile stations). However, note that the same or similartechniques can also be applied in the uplink direction where rectangularburst allocation is used.

In the downlink path, when allocating resources from the frequency-timespace, different rectangular regions within the frequency-time space areallocated to different data bursts. A shaping algorithm is applied by ascheduler of the base station to shape the rectangular regions fordifferent data bursts, in which the criterion for shaping therectangular regions is that the frequency-time space should be as fullyused as possible among the data bursts that are to be communicated frombase station to mobile stations. In addition, the scheduler in the basestation also applies a fitting algorithm to shape the rectangularregions according to a criterion that minimizes (or reduces) data bursterrors.

Moreover, the scheduler in the base station is also able to determinewhether or not one or more data bursts are unable to fit into theavailable space of the frequency-time space due to the shapings appliedby the shaping and fitting algorithms. If that is the case, then thescheduler is able to relax the criteria used by either the shapingalgorithm or the fitting algorithm, or both, to allow for more databursts to be allocated to regions in the frequency-time space.

FIG. 1 illustrates example mobile stations 100 and an example basestation 102 in a wireless network that implements an OFDMA technology.One such example wireless network is the Worldwide Interoperability forMicrowave Access (WiMax) network. In other implementations, other typesof wireless networks can also use the OFDMA technology.

The base station 102 can be connected to other network nodes (not shown)to enable communication between the mobile station 100 and an externalnetwork or another mobile station in the wireless network. The externalnetwork can be a packet data network such as the Internet, a local areanetwork (LAN), a wide area network (WAN), and so forth.

The base station 102 includes a wireless transceiver 104 to performwireless communications (e.g., radio frequency communications) over awireless link 106 with the mobile station 100. The wirelesscommunications includes downlink communications (108) and uplinkcommunications (110).

The base station 102 also includes a scheduler 112 to allocate resourcesin the frequency-time space to communicate downlink data bursts tomobile nodes. Note that although just one base station 102 is depictedin FIG. 1, the wireless network usually includes multiple base stations.

The scheduler 112 can be part of the medium access control (MAC) layerof the base station 102. The scheduler 112 can be implemented ashardware, such as part of a central processing unit (CPU) 114 in thebase station 102. Alternatively, the scheduler 112 can be implemented assoftware executable on the CPU 114. The base station 102 also includes astorage 116 connected to the CPU 114.

FIG. 2 shows an example frame that is defined by 1,024 subcarriers andspans 5 milliseconds, according to one example implementation. The framedepicted in FIG. 2 is an example of allocation performed in a timedivision duplex (TDD) system. Note that techniques according to someembodiments can also be applied to frequency division duplex (FDD)allocations or any other type of bandwidth allocations.

In the example frame depicted in FIG. 2, the horizontal axis representsthe time axis, whereas the vertical axis represents the frequency axis.Along the frequency axis, 1,024 subcarriers at corresponding differentfrequencies are provided. Along the time axis, multiple OFDMA symbolsare provided, which in this example include 47 symbols. Note that thespecific numbers given for the frame depicted in FIG. 2 are provided forpurposes of example. In other implementations, different numbers ofsymbols and different numbers of subcarriers can be provided to define aframe.

Thus, in the frame of FIG. 2, the 5 millisecond duration is divided into47 symbols. The first symbol 202 is used for the preamble, which is usedby a mobile station to achieve downlink synchronization. The following Dsymbols 204 (31 symbols in the FIG. 2 example) are used to transmit datafrom the base station to the mobile station (downlink). The next Usymbols 206 (15 symbols in the FIG. 2 example) are used to transmit datafrom the mobile station to the base station (uplink). As depicted, databursts (as well as control messages) are assigned to correspondingtwo-dimensional regions of the frequency-time space defined by theframe.

In the example, note that the symbols following the preamble symbol 202are also used to communicate broadcast messages describing downlinkparameters and assignments, which in the example of FIG. 2 include adownlink map (DL-MAP) message 208 and a FCH (frame control header)message 210 for the downlink path. Another control message that isprovided on the downlink path is the UL-MAP message 212. UL-MAP providesthe uplink access definition, and DL-MAP provides the downlink accessdefinition. Both DL-MAP and UL-MAP are MAC management messages that arepoint-to-multipoint messages.

In the frame depicted in FIG. 2, a transmit/receive transition gap (TTG)214 is defined between the uplink and subsequent downlink parts of theframe, where the gap 214 allows time for the base station to switchbetween transmit and receive modes. Following the TTG 214, controlmessages are provided in the initial symbols in the uplink direction,where the control messages include feedback channels 216 and a rangingmessage 218. A receive/transmit transition gap (RTG) 215 is providedbetween the uplink and downlink to allow time for the base station toswitch between transmit and receive modes.

The control messages depicted in FIG. 2 are also provided for purposesof example. In other implementations, other control messages can beprovided in the frame and at different locations in the frame.

As further depicted in FIG. 2, an upper group 220 of subcarriers and alower group 222 of subcarriers are defined as guard bands. Thesubcarriers in the guard bands 220, 222 are not used for communicatingeither control messages or data bursts, and the guard bands are providedto reduce interference from adjacent channels. The center part of theframe between the guard bands 220 and 222 is referred to as an activeregion 224, where resources from this active region 224 can be allocatedto communication of control messages and data bursts in the uplink anddownlink.

The subcarriers in the active region 224 (between the guard bands 220and 222) are configured into groups of subcarriers, where each group isreferred to as a subchannel. In one example, there are 840 subcarriers(including pilot and data subcarriers) between in the active region 224,where these 840 subcarriers can be configured into 30 subchannels on thedownlink and 35 subchannels in the uplink, in one example.

In the active region 224, slots are defined, where a slot can be definedas a region in the frame made up of one subchannel by two OFDMA symbols.A slot is the minimum resource that can be allocated to a mobilestation. In alternative implementations, a slot can be made up ofdifferent numbers of subchannels and OFDMA symbols.

Thus, in the example depicted in FIG. 2, there are 450 slots available,where these 450 slots are allocated to communication of control messagesand data. In allocating slots to data bursts associated with differentmobile stations, the allocation is based on the priority (or quality ofservice) associated with the mobile stations.

In accordance with some embodiments, the data bursts are allocated torectangular regions in the frequency-time space. In the downlink path,the data bursts can be shaped and fitted using a two-dimensional (2D)shaping algorithm and 2D fitting algorithm to meet predefined criteria.As noted above, the predefined criterion used by the shaping algorithmfor shaping rectangular regions of the frequency-time space for databursts is a criterion to optimize (maximize) the amount of thefrequency-time space that is used. The fitting criterion uses acriterion to minimize (or otherwise reduce) data burst errors. Thescheduler 112 is also able to determine if any data burst in thedownlink path cannot be fitted into the available frequency-time space,and in response to such determination, the scheduler 112 is able tore-shape the rectangular regions of the frequency-time space to fit thedata burst(s) that previously could not fit into the frequency-timespace. As noted above, the re-shaping is accomplished by relaxing thecriteria used by the shaping and/or fitting algorithms.

FIG. 3 is a flow diagram of a process of assigning resources in thefrequency-time space by the scheduler 112 (FIG. 1) of the base station102 for downlink information (which includes control messages and databursts). Initially, slots are assigned (at 302) to the control overhead(including, as examples, the control messages 208, 210, and 212 in FIG.1). Next, the 2D shaping algorithm is performed (at 304) to shapeassigned slots for data bursts of each mobile station into a rectangularregion. Details of the 2D shaping performed at 304 is depicted in FIG.4, discussed further below.

As part of the 2D shaping performed at 304, prime factors arecalculated. The prime factors are prime numbers into which the number ofslots assigned to each data burst of a mobile station is divisible. Theprime factors are provided (at 306) to a 2D fitting algorithm.Computation of the prime factors are further discussed below.

Next, the 2D fitting algorithm is performed (at 308) using the primefactors for the data burst of each mobile station. The criterion used bythe 2D fitting algorithm is to minimize or reduce burst errors. Mobilestations can be categorized into fast-moving mobile stations (such asmobile stations in vehicles) or slow-moving mobile stations (such asmobile stations carried by pedestrians). For fast-moving mobilestations, the number of OFDMA symbols allocated is increased, while thenumber of subchannels allocated is decreased. Effectively, forfast-moving mobile stations, the ratio of the width of the rectangularregion to the height of the rectangular region is maximized (to providea wide, flat rectangular region).

On the other hand, for a slow-moving mobile station, a smaller number ofOFDMA symbols are assigned, whereas a larger number of subchannels areassigned. This results in a tall, skinny rectangular region, where theratio of the height of the rectangular region to the width of therectangular region is maximized.

For mobile stations that fall between fast-moving and slow-moving(“intermediate mobile stations”), the rectangular region allocated toeach of such intermediate level stations should be as close to a squareas possible. Fast-moving versus slow-moving mobile stations can becategorized based on predefined thresholds, where a fast-moving mobilestation is defined as a mobile station that is moving at greater than apredefined speed (threshold 1), whereas a slow-moving mobile station isdefined as a mobile station that is moving at slower than a predefinedspeed (threshold 2). Mobile stations that are moving at speeds betweenthreshold 1 and threshold 2 are categorized as intermediate mobilestations.

As depicted in FIG. 3, the scheduler 112 determines (at 310) whether atleast one data burst associated with a mobile station does not fit inthe available frequency-time space. If there is no such data burst thatdoes not fit, then the scheduling of data bursts is completed and theprocess can proceed to scheduling for the next frame.

However, if there is at least one data burst that does not fit in theavailable frequency-time space, then the scheduling rules are relaxed(at 312), and the process proceeds back to repeat tasks 302, 304, and308 according to the relaxed rules so that the assigned rectangularregions can be reshaped to accommodate additional mobile stations in thefrequency-time space. For example, instead of maximizing the ratio ofthe width to the height of the rectangular region for a fast-movingmobile station or maximizing the ratio of the height to the width of therectangular region for a slow-moving mobile station, more relaxed ratioscan be specified. In other words, for a fast-moving mobile station,instead of a flat, wide rectangular region, a less wide and less flatrectangular region can be defined. Similarly, for a slow-moving mobilestation, instead of a tall, skinny rectangular region, a less tall and aless skinny rectangular region can be defined for the slow-moving mobilestation.

The procedure of FIG. 3 is iterated until as many data bursts aspossible can be fit into the available frequency-time space.

FIG. 4 shows a process according to an embodiment of shaping allocatedresources for each mobile station into a rectangular region. For allmobile stations MS(i), i=1, . . . , L, where L represents the number ofdata bursts for the mobile stations, each mobile station MS(i) isprocessed in sequence. Initially, i is set (at 402) to 1. Then, M is set(at 404) to be equal to the number of slots assigned to MS(i), where anumber of slots assigned to MS(i) is an initial number of slots assignedby the scheduler 112.

Next, N is set equal to M (at 406). Then, it is determined (at 408)whether N is greater than 1. If so, then N is divided (at 410)recursively (in a loop) by all prime factors up to a prime number thatis less than min(W,H), where W represents the number of pairs of symbolsin the downlink part of the active region 224 of FIG. 2, and Hrepresents the number of subchannels in the downlink part of the activeregion 224. In the above example, since there are 31 symbols in thedownlink part of the active region 224, W is equal to 31/2=15(fractional part removed). Also, since there are 30 subchannels in thedownlink part of the active region 224, H is equal to 30.

In a specific example, if N=30, then the prime factors would be asfollows: 2, 3, 5. In other words, in the recursive loop performed at410, N=30 is first divided by the prime factor 2 to produce 15, and 15is divided by the prime factor 3 to produce 5, and 5 is divided by theprime factor 5 to produce 1.

Next, it is determined (at 412) whether N (after division by the primefactors at 410) is equal to 1. If so, then the number of slots assignedto MS(i) is exactly divisible by prime factors. On the other hand, if Nis not equal to 1, then the number of slots assigned to MS(i) is notexactly divisible by prime factors, so that M has to be adjusted.

In the case where N is equal to 1, it is determined (at 414) if acumulative correction factor C_Cor is less than zero. Note that C_Cor isinitially set to zero. If not, then the correction factor Cor is set (at416) equal to 1. However, if C_Cor is less than zero, then Cor is set(at 418) equal to −1. As will be explained further below, Cor is used toadjust M, which represents the number of slots assigned to MS(i), in thescenario where M is not exactly divisible by prime factors.

Next, i is incremented (at 420) by 1 and the process returns to 404 forthe next data burst of the next mobile station MS(i).

If M is not equal to 1, as determined at 412, then the value of M isadjusted (at 422) as follows: M=M−Cor. Also, the cumulative correctionfactor C_Cor is adjusted as follows: C_Cor=C_Cor−Cor. If Cor ispositive, then the number of slots assigned to MS(i) is reduced.However, if Cor is negative, then the number of slots assigned to MS(i)is increased.

After adjusting M and C_Cor, it is determined (at 424) if C_Cor is equalto zero, and Cor is equal to −1. If so, then Cor is set to 1 (at 426).If not, no further adjusted computation is performed, and the processreturns to 406 to again determine if M is exactly divisible by primefactors.

As noted above, the prime factors into which M is divisible areidentified and provided to the 2D fitting algorithm (306 in FIG. 3). Inthe example above, where M=30, the prime factors into which M isdivisible are as follows: 2, 3, 5. In the 2D fitting algorithm, if themobile station is a fast mover, then the rectangular region allocated tothe data burst of the fast mover would be 15×2, where 15 is computedfrom 3×5. This provides a wide, flat rectangular region where the ratioof the width to the height of the rectangular region is maximized. Onthe other hand, if the mobile station is a slow mover, then theallocated rectangular region would be 2×15 to maximize the ratio of theheight to width of the rectangular region.

In the example above, if it is determined that at least one data burstof at least one mobile station cannot fit into available space of thefrequency-time space, then rules are relaxed, including the ratio rulesassociated with fast and slow movers. Assuming that the mobile stationin the example above where M=30 is a fast mover, then instead ofassigning a 15×2 rectangular region, the 2D fitting algorithm canattempt to fit the data burst into a 10×3 rectangular region, where 10is computed from 2×5 (prime factors). If this assigned region still doesnot allow for the other data burst to fit, then the data burst of thefast mover is fit into a 6×5 region (where 6 is computed from 2×3).Another rule that is relaxed is that the rectangular regions forintermediate mobile stations do not have to be as square as possible.Note that the fitting algorithm continues to use the identified primefactors to reshape the allocated regions.

Note that the specific values used for the various parameters C_Cor andCor under different scenarios can be varied for other embodiments. Forexample, instead of setting Cor to +1 or −1, Cor can be set to otherpositive or negative numbers. Note that care is taken such that thecumulative correction factor C_Cor over all mobile stations does notexceed the maximum number of slots in a frame.

By using the scheduling procedure described above, a flexible mechanismis provided to allocate rectangular regions in the frequency-time spacesuch that utilization of the frequency-time space is maximized orenhanced.

Instructions of software described above (e.g., scheduler 112 in FIG. 1)are executed on a processor. The processor includes microprocessors,microcontrollers, processor modules or subsystems (including one or moremicroprocessors or microcontrollers), or other control or computingdevices. A “processor” can refer to a single component or to pluralcomponents.

Data and instructions (of the software) are stored in respective storagedevices, which are implemented as one or more computer-readable orcomputer-usable storage media. The storage media include different formsof memory including semiconductor memory devices such as dynamic orstatic random access memories (DRAMs or SRAMs), erasable andprogrammable read-only memories (EPROMs), electrically erasable andprogrammable read-only memories (EEPROMs) and flash memories; magneticdisks such as fixed, floppy and removable disks; other magnetic mediaincluding tape; and optical media such as compact disks (CDs) or digitalvideo disks (DVDs).

In the foregoing description, numerous details are set forth to providean understanding of the present invention. However, it will beunderstood by those skilled in the art that the present invention may bepracticed without these details. While the invention has been disclosedwith respect to a limited number of embodiments, those skilled in theart will appreciate numerous modifications and variations therefrom. Itis intended that the appended claims cover such modifications andvariations as fall within the true spirit and scope of the invention.

1. A method of allocating resources in an orthogonal frequency domainmultiple access (OFDMA) system, comprising: a wireless device assigningtwo-dimensional rectangular regions in a frequency-time space to databursts associated with mobile stations using at least one predefinedshaping rule; the wireless device determining that at least one databurst does not fit in an available space in the frequency-time space;and in response to the determining, the wireless device reshaping theassigned two-dimensional rectangular regions, wherein reshaping theassigned two-dimensional rectangular region comprises modifying the atleast one predefined shaping rule to adjust a shape of at least onerectangular region specified by the at least one predefined shapingrule.
 2. The method of claim 1, wherein assigning the two-dimensionalrectangular regions in the frequency-time space is based on a criterionthat specifies that the frequency-time space is to be as fully utilizedas possible.
 3. The method of claim 1, further comprising: applying afitting algorithm to further define the two-dimensional rectangularregions, where the fitting algorithm assigns differently shapedtwo-dimensional regions to fast-moving mobile stations and toslow-moving mobile stations.
 4. The method of claim 3, wherein thefitting algorithm uses a criterion that specifies that data burst errorsis to be reduced.
 5. The method of claim 3, wherein the fittingalgorithm increases a ratio of a width of the rectangular region to aheight of the rectangular region for a mobile station that is fastmoving, and increases a ratio of a height of the rectangular region to awidth of the rectangular region for a mobile station that is slowmoving.
 6. The method of claim 5, wherein the fitting algorithmspecifies that the corresponding two-dimensional rectangular region isto be as close as possible to a square for a mobile station that isneither fast moving nor slow moving.
 7. The method of claim 1, furthercomprising: dividing a number of slots in the two-dimensionalrectangular region allocated to each mobile station by prime factors;providing the prime factors to a fitting algorithm; and using, by thefitting algorithm, the prime factors to further shape thetwo-dimensional rectangular regions.
 8. The method of claim 7, furthercomprising using combinations of the prime factors to define a heightand a width of the two-dimensional rectangular region for each mobilestation.
 9. The method of claim 8, wherein using the prime factors tofurther shape the two-dimensional rectangular region for each mobilestation comprises: using the prime factors to define a wide, flatrectangular region for a fast-moving mobile station; and using the primefactors to define a tall, skinny rectangular region for a slow-movingmobile station.
 10. The method of claim 7, further comprising:determining whether the number of slots is exactly divisible by theprime factors; in response to determining that the number of slots isnot exactly divisible by the prime factors, adjusting the number ofslots in the corresponding two-dimensional rectangular region.
 11. Themethod of claim 1, wherein assigning the two-dimensional rectangularregions in the frequency-time space comprises assigning thetwo-dimensional rectangular regions for downlink data bursts.
 12. A basestation comprising: a wireless transceiver, configured to communicatewith mobile stations; and processing hardware coupled to the wirelesstransceiver, wherein the processing hardware is configured to implementa scheduler, wherein the scheduler is configured to: assign data burstsassociated with mobile stations communicated with the base station totwo-dimensional rectangular regions in a frequency-time space; and shapethe two-dimensional rectangular regions based on speeds of the mobilestations.
 13. The base station of claim 12, wherein the scheduler isconfigured to further: determine that at least one data burst does notfit in an available space in the frequency-time space; and in responseto the determining, reshaping the assigned two-dimensional rectangularregions.
 14. The base station of claim 13, wherein the scheduler isconfigured to further relax rules associated with shaping thetwo-dimensional rectangular regions according to the speeds of themobile stations in reshaping the assigned two-dimensional rectangularregions.
 15. A non-transitory, computer-readable storage mediumcontaining program instructions executable by a processor to: assigntwo-dimensional rectangular regions in a frequency-time space to databursts associated with mobile stations using at least one predefinedshaping rule; determine that at least one data burst does not fit in anavailable space in the frequency-time space; and in response to thedetermining, reshape the assigned two-dimensional rectangular regions,wherein reshaping the assigned two-dimensional rectangular regioncomprises modifying the at least one predefined shaping rule to adjust ashape of at least one rectangular region specified by the at least onepredefined shaping rule.
 16. The non-transitory, computer-readablestorage medium of claim 15, wherein the program instructions are furtherexecutable to: apply a fitting algorithm to further shape thetwo-dimensional rectangular regions, where the fitting algorithm shapesthe two-dimensional regions according to speeds of the mobile stations.17. The non-transitory, computer-readable storage medium of claim 16,wherein the fitting algorithm increases a ratio of a width of therectangular region to a height of the rectangular region for a mobilestation that is fast moving, and increases a ratio of a height of therectangular region to a width of the rectangular region for a mobilestation that is slow moving.
 18. The non-transitory, computer-readablestorage medium of claim 17, wherein the fitting algorithm specifies thatthe corresponding two-dimensional rectangular region is to be as closeas possible to a square for a mobile station that is neither fast movingnor slow moving.
 19. The non-transitory, computer-readable storagemedium of claim 15, wherein the program instructions are furtherexecutable to: divide a number of slots in the two-dimensionalrectangular region allocated to each mobile station by prime factors;provide the prime factors to a fitting algorithm; and use, by thefitting algorithm, the prime factors to further shape thetwo-dimensional rectangular regions.
 20. The non-transitory,computer-readable storage medium of claim 15, wherein the programinstructions are further executable to: use combinations of the primefactors to define a height and a width of the two-dimensionalrectangular region for each mobile station.